SLEEFPirates.jl

ilogbk(x) -> Int

Returns the integral part of the logarithm of |x|, using 2 as base for the logarithm; in other words this returns the binary exponent of x so that

x = significand × 2^exponent

where significand ∈ [1, 2).

ldexpk(a, n)

Computes a × 2^n.

A helper function for ldexpk

First note that r = (q >> n) << n clears the lowest n bits of q, i.e. returns 2^n where n is the largest integer such that q >= 2^n

For numbers q less than 2^m the following code does the same as the above snippet r = ( (q>>v + q) >> n - q>>v ) << n For numbers larger than or equal to 2^v this subtracts 2^n from q for q>>n times.

The function returns q(input) := q(output) + offset*r

In the code for ldexpk we actually use m = ( (m>>n + m) >> n - m>>m ) << (n-2). So that x has to be multplied by u four times x = x*u*u*u*u to put the value of the offset exponent amount back in.

acos(x)

Compute the inverse cosine of x, where the output is in radians.

acos_fast(x)

Compute the inverse cosine of x, where the output is in radians.

acosh(x)

Compute the inverse hyperbolic cosine of x.

asin(x)

Compute the inverse sine of x, where the output is in radians.

asin_fast(x)

Compute the inverse sine of x, where the output is in radians.

asinh(x)

Compute the inverse hyperbolic sine of x.

atan(x)

Compute the inverse tangent of x, where the output is in radians.

atan(x, y)

Compute the inverse tangent of x/y, using the signs of both x and y to determine the quadrant of the return value.

atan_fast(x)

Compute the inverse tangent of x, where the output is in radians.

atan2_fast(x, y)

Compute the inverse tangent of x/y, using the signs of both x and y to determine the quadrant of the return value.

atanh(x)

Compute the inverse hyperbolic tangent of x.

cbrt(x)

Return x^{1/3}. The prefix operator ∛ is equivalent to cbrt.

cbrt_fast(x)

Return x^{1/3}.

cos(x)

Compute the cosine of x, where the output is in radians.

cos_fast(x)

Compute the cosine of x, where the output is in radians.

cosh(x)

Compute hyperbolic cosine of x.

Algorithm:

    movsxd  rax, edi
    imul    rax, rax, 1431655766
    mov     rcx, rax
    shr     rcx, 63
    shr     rax, 32
    add     eax, ecx
    ret

hypot(x,y)

Compute the hypotenuse \sqrt{x^2+y^2} avoiding overflow and underflow.

ilogb(x)

Returns the integral part of the logarithm of abs(x), using base 2 for the logarithm. In other words, this computes the binary exponent of x such that

x = significand × 2^exponent,

where significand ∈ [1, 2).

• Exceptional cases (where Int is the machine wordsize)
  • x = 0 returns FP_ILOGB0
  • x = ±Inf returns INT_MAX
  • x = NaN returns FP_ILOGBNAN

log(x)

Compute the natural logarithm of x. The inverse of the natural logarithm is the natural expoenential function exp(x)

log10(x)

Returns the base 10 logarithm of x.

log1p(x)

Accurately compute the natural logarithm of 1+x.

log2(x)

Returns the base 2 logarithm of x.

log_fast(x)

Compute the natural logarithm of x. The inverse of the natural logarithm is the natural expoenential function exp(x)

pow(x, y)

Exponentiation operator, returns x raised to the power y.

sin(x)

Compute the sine of x, where the output is in radians.

sin_fast(x)

Compute the sine of x, where the output is in radians.

sincos(x)

Compute the sin and cosine of x simultaneously, where the output is in radians, returning a tuple.

sincos_fast(x)

Compute the sin and cosine of x simultaneously, where the output is in radians, returning a tuple.

sinh(x)

Compute hyperbolic sine of x.

tan(x)

Compute the tangent of x, where the output is in radians.

tan_fast(x)

Compute the tangent of x, where the output is in radians.

tanh(x)

Compute hyperbolic tangent of x.